Operational quantities

Antonio Martinón

Commentationes Mathematicae Universitatis Carolinae (1997)

  • Volume: 38, Issue: 3, page 471-484
  • ISSN: 0010-2628

Abstract

top
In this paper we consider maps called operational quantities, which assign a non-negative real number to every operator acting between Banach spaces, and we obtain relations between the kernels of these operational quantities and the classes of operators of the Fredholm theory.

How to cite

top

Martinón, Antonio. "Operational quantities." Commentationes Mathematicae Universitatis Carolinae 38.3 (1997): 471-484. <http://eudml.org/doc/22281>.

@article{Martinón1997,
abstract = {In this paper we consider maps called operational quantities, which assign a non-negative real number to every operator acting between Banach spaces, and we obtain relations between the kernels of these operational quantities and the classes of operators of the Fredholm theory.},
author = {Martinón, Antonio},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {operational quantities; Fredholm theory; Fredholm theory; strictly singular operator; upper semi-Fredholm operator},
language = {eng},
number = {3},
pages = {471-484},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Operational quantities},
url = {http://eudml.org/doc/22281},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Martinón, Antonio
TI - Operational quantities
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1997
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 38
IS - 3
SP - 471
EP - 484
AB - In this paper we consider maps called operational quantities, which assign a non-negative real number to every operator acting between Banach spaces, and we obtain relations between the kernels of these operational quantities and the classes of operators of the Fredholm theory.
LA - eng
KW - operational quantities; Fredholm theory; Fredholm theory; strictly singular operator; upper semi-Fredholm operator
UR - http://eudml.org/doc/22281
ER -

References

top
  1. Fajnshtejn A.S., On measures of noncompactness of linear operators and analogs of the minimal modulus for semi-Fredholm operators (in Russian), Spektr. Teor. Oper. 6 (1985), 182-195. (1985) Zbl0634.47010
  2. Galaz-Fontes F., Measures of noncompactness and upper semi-Fredholm perturbation theorems, Proc. Amer. Math. Soc. 118 (1993), 891-897. (1993) Zbl0782.47013MR1151810
  3. Goldberg S., Unbounded Linear Operators, McGraw-Hill, New York, 1966. Zbl1152.47001MR0200692
  4. González M., Martinón A., Operational quantities derived from the norm and measures of noncompactness, Proc. R. Ir. Acad. 91 A (1991), 63-70. (1991) Zbl1232.47043MR1173159
  5. González M., Martinón A., Operational quantities derived from the norm and generalized Fredholm theory, Comment. Math. Univ. Carolinae 32 (1991), 645-657. (1991) Zbl0762.47005MR1159811
  6. González M., Martinón A., Fredholm theory and space ideals, Boll. U.M.I. 7 B (1993), 473-488. (1993) Zbl0784.47022MR1223653
  7. González M., Martinón A., Note on operational quantities and the Mil'man isometry spectrum, Rev. Acad. Canar. Cienc. 3 (1991), 103-111. (1991) Zbl0779.47012MR1175602
  8. González M., Martinón A., On incomparability of Banach spaces, in: Functional Analysis and Operator Theory, pp. 161-174, Banach Center Publications, vol. 30, Institute of Mathematics, Polish Academy of Sciences, Warzawa, 1994. Zbl0819.46009MR1285605
  9. González M., Martinón A., Operational quantities characterizing the semi-Fredholm operators, Studia Math. 114 (1995), 13-27. (1995) Zbl0830.47008MR1330214
  10. Lebow A., Schechter M., Semigroups of operators and measures of noncompactness, J. Funct. Anal. 7 (1971), 1-26. (1971) Zbl0209.45002MR0273422
  11. Martinón A., Generating real maps on a biordered set, Comment. Math. Univ. Carolinae 32 (1991), 265-272. (1991) Zbl0757.47013MR1137787
  12. Pietsch A., Operators Ideals, North-Holland, Amsterdam, 1980. Zbl0294.47019MR0582655
  13. Rakocevic V., Measures of non-strict-singularity of operators, Mat. Vesnik 35 (1983), 79-82. (1983) Zbl0532.47006MR0724182
  14. Schechter M., Quantities related to strictly singular operators, Indiana Univ. Math. J. 21 (1972), 1061-1071. (1972) Zbl0274.47007MR0295103
  15. Schechter M., Whitley R., Best Fredholm perturbation theorems, Studia Math. 90 (1988), 175-190. (1988) Zbl0611.47010MR0959522
  16. Sedaev A.A., The structure of certain linear operators (in Russian), Mat. Issled. 5 (1970), 166-175. MR 43#2540; Zbl 247#47005. (1970) Zbl0233.46038MR0276800
  17. Tylli H.-O., On the asymptotic behaviour of some quantities related to semi-Fredholm operators, J. London Math. Soc. (2) 31 (1985), 340-348. (1985) Zbl0582.47004MR0809955
  18. Weis L., Über striktle singulare und striktle cosingulare Operatoren in Banachräumen, Diss., Univ. Bonn, 1974. 
  19. Zemánek J., Geometric characteristics of semi-Fredholm operators and their asymptotic behaviour, Studia Math. 80 (1984), 219-234. (1984) Zbl0556.47008MR0783991

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.